>>tromp+(OP)
Even a single bit may be arbitrarily large, depending on the encoding. Encoding may be defined as a language, Turing machine, bb, etc. I can also define a single set bit as 10↑↑100 and beat your busy beaver. It's all arbitrary. A float is also an encoding, and with different mantissa size I may get a larger number.
Now if we count a number of distinct states 64 bits can take, it will still be 18446744073709551615, which I consider the only possible answer.